A pair-density-wave (PDW) is a close relative of the famous FFLO states [1]}, [2]} that arise (at least in theory) in conventional superconductors in response to a small degree of spin-polarization. As the name suggests, this is a superconducting state with a pair-field that is spatially modulated:
\(\big \langle \, c^\dagger _{j,\uparrow } c^{\vphantom{\dagger }}_{k,\downarrow } + c^\dagger _{k,\uparrow } c^{\vphantom{\dagger }}_{j,\downarrow }\,\big \rangle = \Phi (\mathbf {R}^{\vphantom{\dagger }}_j,\mathbf {R}^{\vphantom{\dagger }}_k) \ne 0\quad ,\) 
